I still plan to pursue this line of investigation. Time and money are limiters of course. From their external appearance the made for aquaria designs have either no diaphragms or very small ones. Instead they appear to have a large stem connected to a piston which is acted on by the pressure spring. I think that has a couple of problems.
First, the piston needs a seal for its movement usually an o-ring which by its nature is quite lossy both in friction and static friction, aka "stiction". That will make the response to output pressure flow rather erratic. If you're filling a party balloon or a bicycle tire that probably isn't an issue. The diaphragm needs no such friction-inducing seal since it flexes the small movement amount necessary for opening and closing the poppet/seat closure.
Second, the ratio of areas of the piston and orifice are too close in size to make the piston a large enough contributor in offsetting the spring force. It obviously has an effect since the spring is eventually overcome to maintain the pressure in the output chamber but too small to ensure that it can stabilize the output pressure as the tank pressure falls.
I plan to obtain (as funds permit) a few single stage regulators that appear to be prototypical of the various styles, test them for output stability and publish the results. I also plan to disassemble them to see if I can correlate design features to their performance.
I have two single stage regulators now in hand, one designed "for aquarium use" and another apparently designed as an inflator.
The inflator is a Western Enterprises RP320030. I can't seem to create a direct link to it so
http://www.westernenterprises.com/ and wander around a bit until you find it.
I can't seem to find the name of the aquarium one just now but it is German made. I currently have it on a 24oz paintball tank while I finish my 20lb CO2 setup. The output pressure is fixed on this one at 1.5bar which isn't a bad choice but the needle valve must be more like 5* taper and with a too coarse thread pitch for useful adjustment. Since my solenoid is not yet hooked up I use this needle valve as an on/off control with an inline NV-55 as the actual rate controller.
Jim